Question

A multiple regression model is to be constructed to model the time spent using the internet per week among internet users. The explanatory variables are age, hours spent working per week and annual income.

Data has been collected on 30 randomly selected individuals:

Time using internet (minutes)	Age	Hours working per week	Annual income ('000)
140	56	39	28
257	35	31	79
163	35	35	34
115	33	52	27
182	45	36	37
214	51	57	80
187	44	37	50
142	26	55	41
251	19	47	35
203	21	42	36
243	28	25	26
244	23	26	28
131	48	56	46
174	24	54	63
131	51	52	78
178	38	39	79
135	22	50	36
124	31	57	27
173	57	44	60
189	33	35	58
179	59	30	35
230	37	27	51
121	59	46	53
150	36	40	49
151	42	47	80
147	38	56	35
195	54	32	59
134	58	52	44
190	39	28	27
197	58	40	72

a.) Find the multiple regression equation using all three explanatory variables. Assume that x₁ is age, x₂ is hours working per week and x₃ is annual income. Give your answers to 3 decimal places.

y^ = _____ + _______age + ________ hours working + ________ annual income

b.) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis (is) (is not) rejected.

c.) The value of R² for this model, to 3 decimal places, is equal to __________

d.) The value of s for this model, to 3 decimal places, is equal to _________

e.) The least significant explanatory variable in this model is:

a.) age
b.) hours working per week
c.) annual income

f.) Construct a new multiple regression model by removing the variable annual income. Give your answers to 3 decimal places.

The new regression model equation is:

y^ = ________ + _________ age + ________ hours working

g.) In the new model compared to the previous one, the value of R² (to 3 decimal places) is:

a.) increased
b.) decreased
c.) unchanged

h.) In the new model compared to the previous one, the value of s (to 3 decimal places) is:

a.) increased
b.) decreased
c.) unchanged

i.) The better model is the:

a.) original model
b.) reduced model

Answer 1